Till Hofmann

Daniel Swoboda, Till Hofmann, Tarik Viehmann et al.

Reasoning and planning for mobile robots is a challenging problem, as the world evolves over time and thus the robot's goals may change. One technique to tackle this problem is goal reasoning, where the agent not only reasons about its actions, but also about which goals to pursue. While goal reasoning for single agents has been researched extensively, distributed, multi-agent goal reasoning comes with additional challenges, especially in a distributed setting. In such a context, some form of coordination is necessary to allow for cooperative behavior. Previous goal reasoning approaches share the agent's world model with the other agents, which already enables basic cooperation. However, the agent's goals, and thus its intentions, are typically not shared. In this paper, we present a method to tackle this limitation. Extending an existing goal reasoning framework, we propose enabling cooperative behavior between multiple agents through promises, where an agent may promise that certain facts will be true at some point in the future. Sharing these promises allows other agents to not only consider the current state of the world, but also the intentions of other agents when deciding on which goal to pursue next. We describe how promises can be incorporated into the goal life cycle, a commonly used goal refinement mechanism. We then show how promises can be used when planning for a particular goal by connecting them to timed initial literals (TILs) from PDDL planning. Finally, we evaluate our prototypical implementation in a simplified logistics scenario.

Dillon Z. Chen, Till Hofmann, Toryn Q. Klassen et al.

Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems. We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal plan for each goal atom in some order, perform goal regression on the resulting plans, and lift the corresponding outputs to obtain a set of first-order $\textit{Condition} \rightarrow \textit{Actions}$ rules. The rules collectively constitute a generalised plan that can be executed as is or alternatively be used to prune the planning search space. We formalise and prove the conditions under which our method is guaranteed to learn valid generalised plans and state space pruning axioms for search. Experiments demonstrate significant improvements over state-of-the-art (generalised) planners with respect to the 3 metrics of synthesis cost, planning coverage, and solution quality on various classical and numeric planning domains.

Till Hofmann, Vaishak Belle

Abstraction is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation calculus has focused on non-probabilistic domains, we describe an approach to abstraction of probabilistic and dynamic systems. Based on a variant of the situation calculus with probabilistic belief, we define a notion of bisimulation that allows to abstract a detailed probabilistic basic action theory with noisy actuators and sensors by a possibly non-stochastic basic action theory. By doing so, we obtain abstract Golog programs that omit unnecessary details and which can be translated back to a detailed program for actual execution. This simplifies the implementation of noisy robot programs, opens up the possibility of using non-stochastic reasoning methods (e.g., planning) on probabilistic problems, and provides domain descriptions that are more easily understandable and explainable.

Till Hofmann, Vaishak Belle

A robot's actions are inherently stochastic, as its sensors are noisy and its actions do not always have the intended effects. For this reason, the agent language Golog has been extended to models with degrees of belief and stochastic actions. While this allows more precise robot models, the resulting programs are much harder to comprehend, because they need to deal with the noise, e.g., by looping until some desired state has been reached with certainty, and because the resulting action traces consist of a large number of actions cluttered with sensor noise. To alleviate these issues, we propose to use abstraction. We define a high-level and nonstochastic model of the robot and then map the high-level model into the lower-level stochastic model. The resulting programs are much easier to understand, often do not require belief operators or loops, and produce much shorter action traces.

Till Hofmann, Stefan Schupp

While Golog is an expressive programming language to control the high-level behavior of a robot, it is often tedious to use on a real robotic system. On an actual robot, the user needs to consider low-level details, such as enabling and disabling hardware components, e.g., a camera to detect objects for grasping. In other words, high-level actions usually pose implicit temporal constraints on the low-level platform, which are typically independent of the concrete program to be executed. In this paper, we propose to make these constraints explicit by modeling them as MTL formulas, which enforce the execution of certain low-level platform operations in addition to the main program. Based on results from timed automata controller synthesis, we describe a method to synthesize a controller that executes both the high-level program and the low-level platform operations concurrently in order to satisfy the MTL specification. This allows the user to focus on the high-level behavior without the need to consider low-level operations. We present an extension to Golog by clocks together with the required theoretical foundations as well as decidability results.

Dillon Z. Chen, Till Hofmann, Toryn Q. Klassen et al.

We tackle the challenge of building embodied AI agents that can reliably solve long-horizon planning problems. Imitation learning from demonstrations has shown itself to be effective in training robots to solve a diversity of complex tasks requiring fine motor control and manipulation over low-level (LL), continuous environments. Yet, it remains a difficult endeavour to generate long-horizon plans from imitation learning alone. In contrast, high-level (HL), symbolic abstractions facilitate efficient and interpretable long-horizon planning. We propose to combine the strengths of LL imitation learning for manipulation and control, and HL symbolic abstractions for long-horizon planning. We realise this idea via \emph{bilevel policies} of the form $(π^{\mathrm{hl}}, π^{\mathrm{ll}})$, consisting of a neural policy $π^{\mathrm{ll}}$ learned from LL demonstrations, and an HL symbolic policy $π^{\mathrm{hl}}$ that is constructed from symbolic abstractions of the LL demonstrations combined with inductive generalisation. We implement these ideas in the BISON system. Experiments on extended MetaWorld benchmarks demonstrate that BISON generalises to long horizons and problems with greater numbers of objects than those solved by VLA and end-to-end methods, and is more time and memory efficient in training and inference. Notably, when ignoring LL execution, BISON's HL policies can solve HL problems with 10,000 relevant objects in under a minute. Project page: https://dillonzchen.github.io/bison

Till Hofmann, Hector Geffner

General policies represent reactive strategies for solving large families of planning problems like the infinite collection of solvable instances from a given domain. Methods for learning such policies from a collection of small training instances have been developed successfully for classical domains. In this work, we extend the formulations and the resulting combinatorial methods for learning general policies over fully observable, non-deterministic (FOND) domains. We also evaluate the resulting approach experimentally over a number of benchmark domains in FOND planning, present the general policies that result in some of these domains, and prove their correctness. The method for learning general policies for FOND planning can actually be seen as an alternative FOND planning method that searches for solutions, not in the given state space but in an abstract space defined by features that must be learned as well.

Till Hofmann, Stefan Schupp, Gerhard Lakemeyer

Representing time is crucial for cyber-physical systems and has been studied extensively in the Situation Calculus. The most commonly used approach represents time by adding a real-valued fluent $\mathit{time}(a)$ that attaches a time point to each action and consequently to each situation. We show that in this approach, checking whether there is a reachable situation that satisfies a given formula is undecidable, even if the domain of discourse is restricted to a finite set of objects. We present an alternative approach based on well-established results from timed automata theory by introducing clocks as real-valued fluents with restricted successor state axioms and comparison operators. %that only allow comparisons against fixed rationals. With this restriction, we can show that the reachability problem for finite-domain basic action theories is decidable. Finally, we apply our results on Golog program realization by presenting a decidable procedure for determining an action sequence that is a successful execution of a given program.

Till Hofmann

When reasoning about actions, e.g., by means of task planning or agent programming with Golog, the robot's actions are typically modeled on an abstract level, where complex actions such as picking up an object are treated as atomic primitives with deterministic effects and preconditions that only depend on the current state. However, when executing such an action on a robot it can no longer be seen as a primitive. Instead, action execution is a complex task involving multiple steps with additional temporal preconditions and timing constraints. Furthermore, the action may be noisy, e.g., producing erroneous sensing results and not always having the desired effects. While these aspects are typically ignored in reasoning tasks, they need to be dealt with during execution. In this thesis, we propose several approaches towards closing this gap.

Till Hofmann, Gerhard Lakemeyer

Executing a Golog program on an actual robot typically requires additional steps to account for hardware or software details of the robot platform, which can be formulated as constraints on the program. Such constraints are often temporal, refer to metric time, and require modifications to the abstract Golog program. We describe how to formulate such constraints based on a modal variant of the Situation Calculus. These constraints connect the abstract program with the platform models, which we describe using timed automata. We show that for programs over finite domains and with fully known initial state, the problem of synthesizing a controller that satisfies the constraints while preserving the effects of the original program can be reduced to MTL synthesis. We do this by constructing a timed automaton from the abstract program and synthesizing an MTL controller from this automaton, the platform models, and the constraints. We prove that the synthesized controller results in execution traces which are the same as those of the original program, possibly interleaved with platform-dependent actions, that they satisfy all constraints, and that they have the same effects as the traces of the original program. By doing so, we obtain a decidable procedure to synthesize a controller that satisfies the specification while preserving the original program.